The Lightning won the shootout 2-0, getting goals from Stamkos and Brayden Point.
Stamkos and Victor Hedman each had a pair of goals in regulation. Dan Girardi and J.T. Miller also scored.
NHL leading scorer Nikita Kucherov, returning after missing two games, and Stamkos had three assists apiece. Hedman had two.
Nolan Patrick, Jakub Voracek, Robert Hagg, Jori Lehtera, Ivan Provorov and Claude Giroux scored for Philadelphia.
Tampa Bay goalie Andrei Vasilevskiy recorded 37 saves, while Petr Mrazek made 29 for the Flyers.
The overtime game was Tampa Bay's fifth straight.
With Vasilevskiy having committed a slashing penalty, Giroux slipped a pass to Patrick that the rookie tipped in for his 10th goal and fifth in his last seven games at 7:08 of the first period. Giroux's assist lifted him past Tim Kerr and into sixth place all time with the franchise.
The Lightning tied it at 8:16 when Stamkos one-timed his 26th goal from the middle of the left circle while on the power play.
Voracek put in his own rebound for his 14th goal at 14:30 after a turnover as the Lightning were trying to start a breakout near Vasilevskiy.
Hagg made it 3-1 by scoring his third goal after firing a shot from the high slot at 18:07.
Hedman scored at 5:57 of the second from a bad angle for his 10th goal to make it 3-2.
Girardi blasted his fourth goal at 12:47 to tie it at 3.
It was the 50th career goal for Girardi and the first of his career against Philadelphia in 61 games.
Lehtera beat Vasilevskiy with his second goal at 16:15 while on a delayed penalty.
Provorov scored his 12th at 1:06 of the third for a 5-3 lead, but Miller scored his 14th overall and first as a Lightning at 4:23.
Stamkos' second goal at 7:38 tied it 5-5.
Hedman scored at 10:03 of the period, but Giroux's 23rd goal at 17:07 tied it at 6.
-- Field Level Media
Philadelphia | Tampa Bay | |
Ivan Provorov 3 | Points | Steven Stamkos 5 |
Ivan Provorov 1 | Goals | Steven Stamkos 2 |
Ivan Provorov 2 | Assists | Steven Stamkos 3 |
Nolan Patrick 1 | Power Play Goals | Steven Stamkos 1 |
N/A | Short Handed Goals | N/A |
Petr Mrazek .829 | Save Percentage | Andrei Vasilevskiy .860 |
Petr Mrazek 29 | Saves | Andrei Vasilevskiy 37 |
Team | Shots | Goals | Power Play | Penalty Kill | Penalty Mins | Face Offs Won |
Philadelphia | 43 | 6 | 1-5 | 0-1 | 4 | 40 |
Tampa Bay | 35 | 7 | 1-1 | 4-5 | 12 | 27 |